Question:
Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
Correct Answer
$6858
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5400 × 3% × 9
= $5400 ×3/100 × 9
= 5400 × 3 × 9/100
= 16200 × 9/100
= 145800/100
= $1458
Thus, Simple Interest = $1458
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1458
= $6858
Thus, Amount to be paid = $6858 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5400
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5400 + ($5400 × 3% × 9)
= $5400 + ($5400 ×3/100 × 9)
= $5400 + (5400 × 3 × 9/100)
= $5400 + (16200 × 9/100)
= $5400 + (145800/100)
= $5400 + $1458 = $6858
Thus, Amount (A) to be paid = $6858 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5400, the simple interest in 1 year
= 3/100 × 5400
= 3 × 5400/100
= 16200/100 = $162
Thus, simple interest for 1 year = $162
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $162 × 9 = $1458
Thus, Simple Interest (SI) = $1458
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1458
= $6858
Thus, Amount to be paid = $6858 Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(3) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(7) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?